A294880 Number of divisors of n that are in Perrin sequence, A001608.

0, 1, 1, 1, 1, 2, 1, 1, 1, 3, 0, 3, 0, 2, 2, 1, 1, 2, 0, 3, 2, 2, 0, 3, 1, 1, 1, 2, 1, 4, 0, 1, 1, 2, 2, 3, 0, 1, 2, 3, 0, 3, 0, 2, 2, 1, 0, 3, 1, 3, 3, 1, 0, 2, 1, 2, 1, 2, 0, 5, 0, 1, 2, 1, 1, 3, 0, 3, 1, 4, 0, 3, 0, 1, 2, 1, 1, 3, 0, 3, 1, 1, 0, 4, 2, 1, 2, 2, 0, 5, 1, 1, 1, 1, 1, 3, 0, 2, 1, 3, 0, 4, 0, 1, 3

Offset

1,6

Links

Antti Karttunen, Table of n, a(n) for n = 1..24914

Formula

a(n) = Sum_{d|n} A294878(d).

a(n) = A294879(n) + A294878(n).

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = -1/5 + Sum_{n>=3} 1/A001608(n) = 1.603595519775230150708... . - Amiram Eldar, Jan 01 2024

Example

For n = 22, with divisors [1, 2, 11, 22], both 2 and 22 are in A001608, thus a(22) = 2.
For n = 644, with divisors [1, 2, 4, 7, 14, 23, 28, 46, 92, 161, 322, 644], 2, 7 and 644 are in A001608, thus a(644) = 3.

Mathematica

With[{s = LinearRecurrence[{0, 1, 1}, {3, 2, 5}, 15]}, Table[DivisorSum[n, 1 &, MemberQ[s, #] &], {n, 1, s[[-1]]}]] (* Amiram Eldar, Jan 01 2024 *)

Prog

(PARI)
A001608(n) = if(n<0, 0, polsym(x^3-x-1, n)[n+1]);
A294878(n) = { my(k=1, v); while((v=A001608(k))<n, k++); (v==n); };
A294880(n) = sumdiv(n, d, A294878(d));

Crossrefs

Cf. A001608, A014981, A074788, A294878, A294879.

Cf. also A005086, A293431.

Sequence in context: A246270 A265752 A125090 * A212219 A073266 A125692

Adjacent sequences: A294877 A294878 A294879 * A294881 A294882 A294883

Keyword

nonn

Author

Antti Karttunen, Nov 10 2017

Status

approved